Meteoritics & Planetary Science 39, Nr 10, 1605–1626 (2004) Abstract available online at http://meteoritics.org
Entry dynamics and acoustics/infrasonic/seismic analysis for the Neuschwanstein meteorite fall
D. O. REVELLE,1* P. G. BROWN,2 and P. SPURN›3
1Los Alamos National Laboratory, P.O. Box 1663, MS D401, Los Alamos, New Mexico 87545, USA 2Canada Research Chair in Meteor Science, Department of Physics and Astronomy, University of Western Ontario, London, Ontario N6A 3K7, Canada 3Ondrejov Observatory, Astronomical Institute of the Academy of Sciences of the Czech Republic, 251 65 Ondrejov, Czech Republic *Corresponding author. E-mail: [email protected] (Received 3 November 2003; revision accepted 9 April 2004)
Abstract–We have analyzed several types of data associated with the well-documented fall of the Neuschwanstein meteorites on April 6, 2002 (a total of three meteorites have been recovered). This includes ground-based photographic and radiometer data as well as infrasound and seismic data from this very significant bolide event (Spurn˝ et al. 2002, 2003). We have also used these data to model the entry of Neuschwanstein, including the expected dynamics, energetics, panchromatic luminosity, and associated fragmentation effects. In addition, we have calculated the differential efficiency of acoustical waves for Neuschwanstein and used these values to compare against the efficiency calculated using available ground-based infrasound data. This new numerical technique has allowed the source height to be determined independent of ray tracing solutions. We have also carried out theoretical ray tracing for a moving point source (not strictly a cylindrical line emission) and for an infinite speed line source. In addition, we have determined the ray turning heights as a function of the source height for both initially upward and downward propagating rays, independent of the explicit ray tracing (detailed propagation path) programs. These results all agree on the origins of the acoustic emission and explicit source heights for Neuschwanstein for the strongest infrasonic signals. Calculated source energies using more than four different independent approaches agree that Neuschwanstein was certainly <500 kg in initial mass, given the initial velocity of 20.95 km/s, resulting in an initial source energy ≤0.0157–0.0276 kt TNT equivalent (4.185 × 1012 J). Local source energies at the calculated infrasonic/seismic source altitudes are up to two orders of magnitude smaller than this initial source energy.
INTRODUCTION accomplished only six times before (cf. BoroviËka et al. 2003a)—the orbit of the Neuschwanstein meteorite is The Neuschwanstein meteorite fall occurred at 20:20 UT exceptional in that it is identical to the Pribram meteorite fall on April 6, 2002. The bright fireball that accompanied the of April 7, 1959 (Spurn˝ et al. 2002). This unusual situation is meteorite fall was widely observed in southern Germany, further complicated by the fact that the Neuschwanstein Austria, and the Czech Republic. Of particular interest are the meteorite is an EL chondrite, unlike the Pribram meteorite, photographic recordings of the fireball made from several which was an H chondrite. These data strongly support the German, Czech, and Austrian stations of the European contention of Halliday et al. (1990) concerning the existence fireball network (Spurn˝ et al. 2002) that permit accurate of asteroidal-meteorite streams but poses questions regarding computation of the fireball trajectory and pre-atmospheric the origin of such streams given the dissimilar chemical orbit. In addition to these data, high resolution, radiometric character of these two dynamically related bodies. recordings of the fireball brightness were made at three As part of the multi-instrumental study of the fall of the stations, allowing precise timing and light curve Neuschwanstein meteorite, recordings of the airwave reconstruction. associated with the fireball have been examined. These While recovery of a meteorite with a known orbit is a include infrasonic recordings from Germany and the significant observation in and of itself—this has been Netherlands as well as seismically coupled airwave signatures
1605 © Meteoritical Society, 2004. Printed in USA. 1606 D. O. ReVelle et al. on nine seismographs in the immediate region of the fireball These calculations were accomplished entirely in endpoint. These data permit detailed reconstruction of many Cartesian coordinates (as the entry angle was greater than 10° aspects of the shock production associated with the upward from the horizon) using a hydrostatic, perfectly Neuschwanstein fireball, as the precise path in the atmosphere stratified (along the vertical axis), steady state model can be combined with acoustic propagation modeling to atmosphere that was appropriately modified to correspond to disentangle fragmentation and acoustic radiation patterns. In the typical properties of a U.S. Standard Atmosphere particular, by examining infrasound and seismically coupled (indicative of a summer situation in middle latitudes). Both airwave data in conjunction with modeling, we hope to the ambient atmospheric pressure and the vertical air density determine the source altitude for the acoustic signal observed profiles have been calculated using this atmospheric at each station and measure the extent and location of modeling assumption for all entry model computations. fragmentation points along the trajectory and, therefore, set Finally, we have allowed the temporal/spatial wake limits on the deviation (if any) of the acoustic radiation behavior of all of the fragments to correspond to a state of pattern from the standard bolide cylindrical line source model collective wake action of all of the fragments (one of three (cf. ReVelle 1976) for such fragmentation points. available options in the computer code) such that: Additionally, the propagation channels for each portion of the 1. Either the particles are put into the wake and infrasound signal for proximal stations can be determined, permanently “lost” from a luminosity and deceleration and estimates for the total energy of the fireball can be made standpoint, i.e., they always remain in the wake behind based on these recorded airwave data. the original leading fragment; 2. The fragments are put into the wake and brought back DETAILED ENTRY DYNAMICAL SIMULATIONS forward to increase the frontal area and effect both the FOR NEUSCHWANSTEIN luminosity and the deceleration after a short time delay that is a function of the bolide’s speed; or Starting from flight data given in Spurn˝ et al. (2002, 3. There is also the possibility of an intermediate 2003) and using a newly developed FORTRAN computer condition that accomplishes the last option in a quasi- code (ReVelle 2001, 2002a, b), we have been able to evaluate periodic manner. This has not yet been fully the detailed entry behavior of Neuschwanstein and compute implemented in our code. the corresponding dynamics, energetics, expected The 5% porosity value assumed in the list above is most fragmentation effects, and also make quantitative luminosity likely an upper limit to the “true” value for this bolide, predictions (over the panchromatic pass-band region from especially given its true nature as an EL chondrite (Spurn˝ et 360–675 nm) for the bolide. The full details of this code will al. 2002). In general, as both the volume-weighted porosity be reported shortly, including discussions of newly developed and the final number of fragments are allowed to increase, the concepts that separate the traditional single-body entry predicted luminosity of a given bolide will also increase but dynamics treatment from a more thorough analysis including for differing reasons. Thus, we have varied both of these the fragmentation-dominated flow regime. fundamental parameters independently while maintaining We have used the following input values for the various upper limits on each one separately to determine Neuschwanstein meteorite fall, as largely constrained from the sensitivities in the final result. This is discussed further photographic flight data: initial radius = 0.33 m, with a below. Figures 1–5 give the results for the predicted values corresponding entry velocity = 20.95 km/s at an entry angle of: measured from the zenith of 40.25°. We assumed a maximum • panchromatic stellar magnitude versus time; number of eight fragments for a body (based on observations • mass versus time; in Spurn˝ et al. 2002, 2003) the shape of which was assumed • panchromatic luminosity (watts/steradian) versus time; to be spherical (Sf = 1.209, the shape factor ≡ frontal cross- • height versus velocity; sectional area/volume2/3). For µ, the shape change factor = 2/3 • ablation parameter versus time. (which corresponds to a self-similar solution with no shape The observed peak stellar magnitude (or equivalently, the change allowed), and the corresponding D or energetics predicted panchromatic luminosity in watts/steradian) for this parameter of ReVelle = 4.605 (corresponding to 99% of the combination of parameters agrees quite well with the original kinetic energy available at the “top” of the maximum value proposed by Spurn˝ et al. (2002, 2003). The atmosphere having been depleted at the end of the visible predicted mass behavior (initial mass and final mass, etc.) trajectory). The ablation parameter, σ, is a full function of also agrees well with the observations, as does the final height/time in all of these simulations, and a nominal, volume- velocity of the meteorites just before dark-flight began. weighted porosity was assumed to be equal to 5% (though Table 1 summarizes many of our modeling results for some trial values as large as 10% were also used). However, Neuschwanstein. The final entry dynamics initial source values of µ as small as 0.10 (ReVelle and Ceplecha 2001b) did energy estimate has been found to agree quite well with those not greatly modify the results given above. found using other techniques (see below). Entry dynamics and acoustics/infrasonic/seismic analysis of Neuschwanstein 1607
Fig. 1. Predicted panchromatic stellar magnitude versus time (sec) Fig. 3. Predicted panchromatic luminosity (watts/steradian) versus for Neuschwanstein. time (sec) for Neuschwanstein.
Fig. 4. Predicted height (km) versus velocity (km/s) for Fig. 2. Predicted mass (kg) versus time (sec) for Neuschwanstein. Neuschwanstein.
Infrasonic Recordings generates coherent motion of the atmosphere over large spatial scales (>10s to 100s of m) and/or at high velocities can radiate Infrasound is that portion of the atmospheric acoustic energy in the infrasonic regime. If the horizontal scale of the wave spectrum below ~20 Hz (sub-audible) and above the source is comparable to or exceeds the local pressure (or natural oscillation Brunt-Vaisalla frequency of the atmosphere density) scale height, emissions tend to be concentrated at (>~0.02 s−1 in angular frequency or >~3.2 × 10−3 Hz or gravity wave frequencies rather than in the infrasonic regime, <~311 sec in period) below which internal atmospheric as in the case of the Tunguska event of June 30, 1908. Of gravity waves with generally sub-acoustic propagation particular importance to its utility in long-range detection, the velocities dominate (cf. Beer 1974). Any mechanism that attenuation of infrasonic waves in the lower atmosphere is 1608 D. O. ReVelle et al. very small—acoustic radiation with frequencies below a few station recordings have been employed for bolide geolocation Hz can result in detections at 100s to many 1000s of km, (Brown et al. 2002c). A recent analysis of the Morávka depending on the initial source energy and altitude, meteorite fall (BoroviËka et al. 2003a; Brown et al. 2003) has atmospheric turbulence levels, and winds. placed some limits on characteristics of the shock wave source The long-distance detection of infrasound from fireballs at the fireball from both the ballistic wave and fragmentation has been used previously to determine influx rates for m-sized events, suggesting that the deviation of the ray normals for the bodies (ReVelle 1997, 2002) and for the estimation of bolide fragmentation events may be as much as 30° beyond that energies (ReVelle 1976). Recently, infrasound records have expected from a purely cylindrical line source blast. been combined with satellite data to estimate bolide source The infrasonic signals from the Neuschwanstein fireball energies, luminous efficiencies, and to calibrate influx rates were recorded in Freyung, Germany by station FREYUNG observed by satellite systems (Brown et al. 2002b), while multi- (IS26) (13.7131° E, 48.8516° N, elevation above sea level, h = 1111 m). This station is part of the International Monitoring System (IMS) of the Comprehensive Test Ban Treaty (CTBT) infrasound array located at a distance of 256 km from the point of fireball maximum light (see Spurn˝ et al. 2002). The signals detected at the five low frequency microphones of the IS26 array are shown in Fig. 9. Weak airwaves from the event may also have been detected at the Deelen Infrasound array in the Netherlands (Evers and Haak 2001) at a range of 622 km. IS26 recorded the airwave arrival from the fireball beginning 820 sec after the fireball (20:33:53 UT) and ceasing approximately 100 sec later at 20:35:33 UT. Using the signal from all five elements and applying standard beam-forming techniques to search for maximum cross-correlation within 20 sec bin windows (cf. Evers and Haak 2001), the azimuth of the peak signal cross-correlation and the value of the peak cross-correlation are indicated in Fig. 10. Figures 9 and 10 clearly show that the fireball airwave consists of two distinct portions: an early, impulsive arrival near 820 sec, lasting <10 sec and composed of high frequency energy (>1 Hz), and a larger amplitude signal beginning 1 min Fig. 5. Predicted ablation parameter, σ, (in kg/MJ) versus time (sec) later, consisting of several sub-maxima, lasting longer, and for Neuschwanstein. having a comparably higher frequency. It is notable that,
Table 1. Summary of entry dynamics: Findings for Neuschwanstein. Neuschwanstein meteorite fall results Parameters Initial source energy 0.0157 kt (1 kt = 4.185 × 1012 J) Initial source energy: entry modeling results 0.0276 kt (1 kt = 4.185 × 1012 J); see below Initial mass: (kg) estimate by Spurný et al. (2002, 2003) 300 ± 100 kg Initial radius and mass: (kg) entry modeling 0.33 m, 529.1 kg (0.30 m, 397.5 kg if the total number of fragments is 16–50; see below) Final mass: (kg) independent estimate ≥6.22 kg (1.63, 1.75, and 2.84 kg with a total estimate on the ground = 20 kg). These three meteorites were recovered in very rugged terrain, so it is unlikely that more will be recovered. Final mass: (kg) entry modeling 35.5 kg (28.4 kg for 16–50 total fragments, an initial radius = 0.30 m, an initial mass = 397.5 kg, and an initial source energy = 0.0208 kt) Volume weighted porosity (%) 0–10% (<5% is the nominal best-fit value) Total number of fragments assumed (nominal): assuming 16–50 8; this could not be reliably determined from the photographs at the fragments with a smaller initial radius produce even better agreement closest German EFN station, the optics of which are not comparable with the results of Spurn˝ et al. (2002, 2003). to the standard fish-eye lens used at other stations. Stagnation pressure at significant break-up: observed 4.6 MPa Stagnation pressure at significant break-up: model value 2.90 MPa Semi-empirical, maximum luminous efficiency: differential value 6.9% Entry dynamics and acoustics/infrasonic/seismic analysis of Neuschwanstein 1609 within the second wavetrain, the azimuth bearings for the 5.36 ± 1.94 Pa. While the magnitude of the cross-correlation peak correlation move systematically to lower azimuths falls below the general background level for this bandpass and beginning near 234° and shifting to ~225° some 40 sec after window binning size, the near steady azimuth values from the peak amplitude is reached (see Fig. 10). The peak 810–950 sec indicate substantially longer signal durations amplitude for the first wavetrain (hereafter, wavetrain a) is than the cross-correlation alone would suggest. Indeed, using ~1.55 ± 0.33 Pa, while that for the second (wavetrain b) is other bandpass/window binning combinations produces significant cross-correlations above background over this entire interval. The signal energy between wavetrains a and b
a Fig. 6. Predicted differential acoustic efficiency values and the least- squares curve fit used in this study versus height (km) for Neuschwanstein.
b
Fig. 8. Numerically predicted line source blast radius and concomitant source energy as a function of height simultaneously using the entry dynamics values of the theoretical differential acoustic efficiency, modeled mass, modeled velocity, and entry angle and the observed infrasonic pressure amplitude at the ground; strong infrasound results using a search altitude step = 0.50 km (a) and weak Fig. 7. Predicted entry dynamics line source blast wave relaxation infrasound results using a search altitude step = 1.0 km (b). See text radius (including fragmentation effects) versus height (km) for for an explanation of the new technique. Neuschwanstein. 1610 D. O. ReVelle et al.
Fig. 9. The recorded infrasound signal on all five channels at Freyung for the Neuschwanstein fireball. Note that these waveforms have been high-passed above 0.40 Hz to most clearly define the fireball signal. The time is relative to 20:20:13 UT on April 6, 2002. and the signal after 920 sec in wavetrain b are of minor microphone to the next; the steeper the airwave arrival, the amplitude and may indicate scattering/diffracted acoustic higher the trace velocities) shows no significant trend across energy or could be returns from atmospheric paths extending the signal—these values all lie near 0.33 ± 0.02 km/s, to higher altitudes (and, thus, suffering greater attenuation). implying fairly shallow local arrivals. The examination of the airwave’s apparent trace velocity To link these observed infrasonic data with the (a measure of the signal’s apparent velocity of travel from one Neuschwanstein fireball, we use the accurate trajectory Entry dynamics and acoustics/infrasonic/seismic analysis of Neuschwanstein 1611
Fig. 10. The maximum correlation coefficient during the time centered around the Neuschwanstein fireball signal at Freyung (top). Cross- correlation windows of 20 sec (with 50% overlap per window) are used to define individual measurements of cross-correlation. The background cross-correlation in this frequency bandpass (0.5–8 Hz) is 0.39 ± 0.02. The associated azimuth to maximum cross-correlation is also shown (middle). The amplitude for channel 1 is also shown at the bottom for comparison. information together with a numerical acoustic ray tracing Briefly, the modeling procedure involved shooting rays code to compare model values for arrival angles and timing from each point along the trajectory below 40 km in the with those expected for moving point sources and later for direction of Freyung but with a wide range of elevation ideal line (infinite speed) and modified line sources (finite angles. The computer code used in this effort is called speed compared to the local sound speed) distributed along InfraMap (BBN 2000). The rays were allowed to propagate the trail. through a steady state, range-independent model atmosphere (MSIS-E: mass spectrometer and incoherent scatter model Acoustic Numerical Ray Modeling (Moving Point Source and the horizontal wind model [HWM]; see below for a Model) description of these models). We followed the complete acoustic path for each ray to To simulate acoustic production from the determine the delay time and arrival direction at the receiver of Neuschwanstein fireball, we first treat a large number of those rays passing within 10 km (horizontally or vertically) of individual points along the fireball path, assuming each the receiver array at Freyung. To model these acoustic arrivals, moving point to be a potential producer of acoustic radiation. we made use of the radiosonde data from Munich, Germany 1612 D. O. ReVelle et al.
(~70 km north-northeast from the fireball endpoint) taken at 18 Figs. 12–13. Each point in these simulations represents a UT on April 6, 2002 to define the temperature and wind field single height corresponding to the measured shutter break up to 32 km in altitude. Above 32 km in altitude, we merged positions along the fireball path as described in Spurn˝ et al. these radiosonde data with the MSIS-E model to produce the (2003). Figure 12 shows the time delay for the arrival of temperature profile (cf. Picone et al. 1997) up to a height of rays at Freyung as a function of the source height along the 140 km, inputting the appropriate geomagnetic indices for fireball path. The time delay includes both the propagation April 6, 2002 (which can significantly affect the atmospheric time and a correction for the source generation time due to temperature and, thus, the local sound speed at heights above the finite velocity of the fireball. Figure 13 shows the delay ~100 km). We note that the MSIS-E temperatures below 32 km time as a function of the source height along the fireball were virtually indistinguishable from those of the radiosonde, path and the launch elevation (relative to the horizontal) for except in the lower 3–4 km near the ground, i.e., in the rays reaching Freyung as a function of source height. Based atmospheric boundary layer. The wind field above 32 km was on the maximum height reached by the rays, the type of ray approximated using the HWM (Hedin et al. 1996). The wind path (stratospheric or thermospheric) is given in these field and temperature profiles used are shown in Figs. 11a and figures. 11b. This numerical model has also been used previously for From these figures, it is immediately apparent that the interpreting infrasonic data measured for the Morávka fireball main arrival (wavetrain b) is generated in the lowest portion of (see Brown et al. [2003] for more details). the fireball path, between 16–22 km, centered in the vicinity of The results from these model calculations are shown in the brightest portion of the fireball trajectory. In contrast, the
Fig. 11. Wind profile (a) used in numerical ray modeling and comparison to radiosonde data taken near the time of the event. Entry dynamics and acoustics/infrasonic/seismic analysis of Neuschwanstein 1613
first arrival (wavetrain a) appears to be generated at a height of 30–32 km, which is well before the main detonation. To independently confirm this interpretation, the apparent arrival azimuth for each modeled ray at Freyung as a function of both height and the corrected delay time is given in Fig. 14. The observed azimuths at Freyung at the time of maximum amplitude for each wavetrain are also shown in the figure. It is clear that the later wavetrain b is a stratospheric arrival emanating from almost precisely the brightest segment of the fireball trail. Similarly, wavetrain a is generated from an altitude of 31 ± 1 km. To ascertain the probable source mechanisms involved for both wavetrains, we have plotted in Fig. 15a the launch azimuth for rays reaching Freyung from all heights along the fireball path as a function of the ray launch elevation. For a line source blast wave source model, which approximates well the acoustic radiation expected from a non-fragmenting fireball (cf. ReVelle 1976), the rays are launched perpendicular to the fireball path. The locus of the azimuth and of the altitude pairs fulfilling this condition for Fig. 11. Continued. Temperature (b) used in numerical ray modeling Neuschwanstein are indicated by the dark line in Fig. 15a. and comparison to radiosonde data taken near the time of the event. Comparison of this result with that given in Fig. 13 indicates
Fig. 12. Source generation heights in km at measured shutter-break points along the fireball entry trajectory as a function of modeled arrival times at IS26 (bottom). 1614 D. O. ReVelle et al.
Fig. 13. Ray arrival time delays as a function of generation height (the lines show the extent of significant signal from wavetrains a and b) (top). Ray launch elevation as a function of height along the fireball Fig. 14. The apparent azimuth of arrival for modeled rays at Freyung path (bottom), where T denotes thermospheric returns and S denotes as a function of the source height along the fireball path (top). The stratospheric returns. observed azimuths of peak cross-correlation at maximum amplitude are also shown for each wavetrain. The apparent arrival azimuth as a function of corrected time delay for ray arrivals at IS26 (bottom). The that the main arrival (wavetrain b) is produced by observed values for wavetrain a and b are shown as open squares. stratospheric rays that radiate along the cylindrical line source airwave “path.” These are geometrically ideally suited recently developed ray tracing code that can be run in either to be produced at the fireball source and recorded at Freyung. of two respective limits: a) an infinite speed line source mode The reason that these observed rays are so close to being (with respect to the local adiabatic thermodynamic sound perpendicular in the precise source region where speed at any height); or b) a modified line source mode using fragmentation occurs is not clear, but this is what we have the finite speed of the bolide with respect to the local been able to determine from these calculations. adiabatic thermodynamic sound speed (with this speed ratio In contrast, the acoustic paths from an altitude of 31 ± held constant at all altitudes). 1 km that are responsible for wavetrain a are launched at Both options of the code were used using the identical upward angles near 23° from the horizontal—this is 33° from model atmosphere as above for the moving point source ray perpendicular to the fireball path. The most straightforward tracing efforts to identify various possibilities for ray paths interpretation would be that this represents a major from the bolide for propagation to IS26 (the Freyung fragmentation point for the fireball, as such events are infrasound array). The results shown below were expected to produce quasi-spherical acoustic radiation from a accomplished using only option (a) as described above, i.e., rapidly moving source (cf. Brown et al. 2003). an infinite speed was assumed (or equivalently, an instantaneous energy release). In certain altitude regions Line Source and Modified Line Source Ray Tracing Efforts (where refractive effects are especially large), the detailed propagation path results are quite sensitive to the precise To compliment the above analysis, we also make use of a entry speed assigned to the Neuschwanstein bolide. We have Entry dynamics and acoustics/infrasonic/seismic analysis of Neuschwanstein 1615
Fig. 16. Initial ray launch angle from the horizontal (°) versus the line source entry plane deviation (°) for Neuschwanstein.
severely restricted by the line source cylindrical geometry, which is, in general, described by a very narrow Mach cone at any height for the range of entry speeds being considered (ignoring fragmentation effects). The line source solution geometry with respect to the Neuschwanstein-Freyung propagation path is given in Fig. 16. From this diagram, using the deduced infrasonic arrival azimuths from 225–234° quoted earlier, we have determined that “rays” would need initially to have been launched downward from the source for entry plane deviations from ~60–70° with initial launch angles of ~8–27°. Our detailed results have been binned into the altitude ranges from 50–80 km and 20–50 km for clarity and Fig. 15. a) The azimuth at which modeled rays were launched from are plotted in Figs. 17–22, first for the altitude region of 20– the source (along the fireball path) as a function of the modeled ray launch elevation (relative to the horizontal at 0°). Each point 50 km and, subsequently, for the height range of 50–80 km. represents one ray that is able to reach Freyung from a point along the The respective views that are shown are the top view and the fireball path. The bold line represents those points that are at right various east-west and north-south side views. The complexity angles to the fireball trajectory; b) the vertical seismic component for of the detailed propagation paths at great ranges is quite station SQTA (top) showing airwave arrival near a time delay of obvious from these figures but especially for source heights 145 sec. The bottom plot shows the modeled time delays from point sources distributed along the fireball trajectory (as a function of along the fireball path above the stratopause. For ranges from height). ±~50–200 km for this specific entry trajectory, “rays” (actually the local wave normals, which are different from rays not pursued option (b) fully yet because the computer code when wind effects are properly taken into account) produce an that was recently written only accepts a single constant speed isonified zone on the ground directly below the entry over the entire path at the current time and does not have the trajectory, while at great ranges, subsequent refraction effects built-in capability yet to patch together the various sections of produce distinct zones of silence as well (ignoring diffraction/ the entry trajectory at differing bolide speeds as the body scattering effects). This effect has been well-known for many decelerates. years for bolides and for other sources with respect to ground- The set of equations used to generate these solutions are based sound observations. We have not yet been able to follow identical to those used for the moving point source ray tracing the propagation all the way from the source to the receiver for described earlier, but the set of possible launch angles is this “line” source type propagation since our computer code 1616 D. O. ReVelle et al.
Fig. 17. Top view; line source ray tracing for source altitudes of 20– 50 km for Neuschwanstein. Initially downward rays launched at 24 different azimuths for heights 20–50 km at 1 km intervals; Vinf = Fig. 19. Side view from the east; line source ray tracing for source 20.95 km/s is assumed throughout; theta = 49.75°; heading = altitudes of 20–50 km for Neuschwanstein. Initially downward rays 295.234°. launched at 24 different azimuths for heights 20–50 km at 1 km intervals; Vinf = 20.95 km/s is assumed throughout; theta = 49.75°; heading = 295.234°.
Fig. 18. Side view from the south; line source ray tracing for source Fig. 20. Top view; line source ray tracing for source altitudes of 50– altitudes of 20–50 km for Neuschwanstein. Initially downward rays 80 km for Neuschwanstein. Initially downward rays launched at 24 launched at 24 different azimuths for heights 20–50 km at 1 km different azimuths for heights 50–80 km at 1 km intervals; Vinf = intervals; Vinf = 20.95 km/s is assumed throughout; theta = 49.75°; 20.95 km/s is assumed throughout; theta = 49.75°; heading = heading = 295.234°. 295.234°. Entry dynamics and acoustics/infrasonic/seismic analysis of Neuschwanstein 1617
Fig. 21. Side view from the south; line source ray tracing for source Fig. 23. Contours for downward launched ray turning angles as a altitudes of 50–80 km for Neuschwanstein. Initially downward rays function of the line source ray turning height (km) and the source launched at 24 different azimuths for heights 50–80 km at 1 km altitude (km) for Neuschwanstein. intervals; Vinf = 20.95 km/s is assumed throughout; theta = 49.75°; heading = 295.234°. has not yet been modified to accomplish this entire task, i.e., it currently only calculates the expected “hypersonic boom carpet.” However, we expect that these modifications will soon be accomplished so that the code will be available for future bolide infrasonic and seismic analyses. Finally, we have also used a simpler ray evaluation code to numerically evaluate the full refractive possibilities for the same set of initial atmospheric (temperature and winds, etc.) and bolide data (heading and entry angles). This additional code does not formally compute the actual ray paths between the source and the receiver but simply calculates the expected turning heights using the same model atmosphere as that used for the moving point and line source ray tracing codes described previously. The results for these calculations are given in Fig. 23 for initially downward rays (see below for more details about the blast radius for Neuschwanstein). These results clearly show turning heights (~40–50 km) below a source height of ~35 km due to atmospheric refractive effects as also seen in the earlier ray tracing results for Neuschwanstein.
Seismic Data
In addition to having been detected infrasonically at Fig. 22. Side view from the east; line source ray tracing for source Freyung, the airwave from the Neuschwanstein fireball was altitudes of 50–80 km for Neuschwanstein. Initially downward rays recorded directly on at least nine seismic stations near the launched at 24 different azimuths for heights 50–80 km at 1 km fireball endpoint. Figure 24 shows a ground projection of the intervals; Vinf = 20.95 km/s is assumed throughout; theta = 49.75°; heading = 295.234°. fireball and the location of the seismic stations that show an 1618 D. O. ReVelle et al.
Fig. 24. The ground projection of the Neuschwanstein fireball trajectory showing the location of the seismic stations that detected Fig. 25. The signal spectrum associated with the fireball at seismic the airwave from the fireball. The point of brightest luminosity is station WATA. The acoustic wave arrival is represented by the shown as a solid circle symbol. strong, high frequency signal at 20:23:10 UT. The Rayleigh wavetrains immediately before and after this signal are circled in the airwave signal associated with the event. In all cases, these spectrogram. The ordinate, WATAEHZ, is the measured wave frequency in Hz as a function of the power levels in dB (contoured in seismic data show the direct expression of the airwave black and white). compressing the ground near the seismic station. In addition, acoustically coupled ground waves (Rayleigh) (also height along the fireball trajectory were found that could then commonly called air-coupled Rayleigh waves in the seismic be compared to the observed airwave arrivals at each station. literature) excited proximal to the seismic station are visible as An example of the procedure is shown in Fig. 15b for one lower frequency precursor signals on some stations. Similarly, seismic station. several stations show extended Rayleigh wave trains lasting, The result of this procedure was to constrain the possible in some cases, more than a minute after the passage of the height interval along the fireball path from which the acoustic main airwave. Similar seismic behavior has been observed signal might have been generated. We emphasize that the previously in the case of the Morávka and Tagish Lake acoustic path to the station was not restricted to be fireballs (cf. Brown et al. 2002a, 2003). Figure 25 shows a perpendicular to the fireball trajectory as would be the case spectrogram of the seismic energy for one station, with these for an ideal cylindrical blast source. Rather, we attempted to different features clearly identifiable. define any possible accessible acoustic path to the seismic The character of the signal is different for each station station at each height, irrespective of the source due in part to differences in propagation geometry, source- characteristics. The final best-fit source height and allowable receiver geometry, instrument sensitivities, and ground height intervals based on the spread in ray arrival times are properties near the seismographs. Figure 26 shows the given in Table 3. vertical component of the raw seismic record (uncorrected for Several stations showed secondary maxima within 5– instrumental sensitivity). Table 2 summarizes the seismic 10 sec of the main airwave arrival. The spectral character of stations that recorded signals from the fireball. The time of these signals was not similar to the main airwave arrival. the arrival of the main acoustic wave and the start and end of However, the most notable secondary events are the later the associated Rayleigh wavetrain (if applicable) is maxima detected at seismic stations: FUR, WTTA, and summarized in Table 3. WATA. And, these are all consistent (based on the ray-trace To determine the probable source heights for the acoustic modeling) with a source near 30 km height along the fireball signals recorded at each station, the numerical moving point trajectory. This would be consistent with the smaller signal source ray tracing model used previously to interpret the detected at IS26, which is associated with a possible infrasonic signal at Freyung was again employed. secondary fragmentation source near a height of 31 km. Specifically, rays were shot toward each seismic station (at Alternatively, these secondary events may represent locally 5 km increments in height along the fireball trajectory). The enhanced coupling of acoustic energy into Rayleigh waves, same iterative procedure was used again (as with the possibly as a result of topographical variations or ground infrasound signal arrivals at Freyung) to try to determine the character and its lateral variations. azimuth and altitude of any possible acoustical paths that Figure 27 shows the deviation of the ray launch reached the array. In most cases, several paths were found at directions from the perpendicular for the best-fit modeled each specific height. In this way, a series of time delays versus timing for each station. Error margins represent the range of Entry dynamics and acoustics/infrasonic/seismic analysis of Neuschwanstein 1619
Fig. 26. The raw vertical component of the seismic signals from each station that detected the airwave from the Neuschwanstein fireball. The time is in sec relative to 20:20:13 UT, April 6, 2002. These seismic data have been band-passed to maximize the visibility of the airwave signal; typically, this involves a high-pass filter above 1–2 Hz (depending on the station and local noise characteristics). The signals are uncorrected for seismograph response. allowable directions given the height intervals where timing geometry) was found to be ~25° in the case of the arrivals at matches between the modeled and observed airwave arrivals FUORN and FUR. This is very similar to the maximum agreed within the measurable errors. For almost all signals, deviation found for the Morávka fireball event (Brown et al. the deviations are quite small, typically <5°, with error 2003). It is notable that both seismic stations showed, among margins allowing deviations possibly as high as 10°. The the weakest detectable signals, one that is perhaps a reflection extreme deviations from the perpendicular launch (and, of the non-perpendicular geometry involved. hence, the possible deviation from line source blast wave In general, the computed arrivals were systematically 1– 1620 D. O. ReVelle et al.
Table 2. List of seismic stations that detected the Neuschwanstein fireball. Name Code Network Longitude (°E) Latitude (°N) Altitude (m) Walderalm WATA ZAMG-Austria 11.576 47.336 1492 Wattenberg WTTA ZAMG-Austria 11.636 47.264 1764 Sankt Quirin SQTA ZAMG-Austria 11.209 47.221 1307 Moosalm MOTA ZAMG-Austria 11.104 47.345 1575 Ofenpass FUORN ZUR-Switzerland 10.26352 46.62022 2333 Gräfenberg Array (Böhmfeld) GRC2 BGR-Germany 11.376 48.868 447 Fürstenfeldbruck FUR FUR-Germany 11.275 48.163 565 Schlegeis SCE FUR-Germany 11.7103 47.0386 1737 Gräfenberg Array (Bettbrunn) GRC3 BGR-Germany 11.586 48.890 445
Table 3. Seismic waves: first arrival times at different stations. a c d d e Range Observed acoustic C-O res Ri Rf Height Model launch Model launch Station (km) arrivalb (sec) (sec) (sec) (km) azimuthf altitudef MOTA 24 101 4.16 77 197 20 (18–22) 139.83 −43.35 SQTA 36 143 4.16 117 197 25 (20–25) 146.91 −37.9 WATA 38 177.5 1.42 132 227 40 (35–45) 108.36 −42.55 WTTA 41 192.5 2.40 173 213 42 (40–45) 116.66 −43.2 SCE 57 236 4.40 – 249.4 50 (48–52) 137.82 −36.9 FUR 81 299 0.12 – – 39 (38–41) 4.6 −17.5 FUORN 113 394.5 8.48 – – 40 (40–45) 220.65 −17.7 GRC2 158 544 2.04 – – 45 (35–45) 5.65 −2.1 GRC3 164 553 3.72 – – 40 (35–45) 9.4 8.4 aThe range is the direct distance between the height of the best-fit (based on the arrival time of the acoustic wave at the seismic station) along the fireball trajectory and each seismic station. bThe observed arrival times are in sec relative to 20:20:13 UT on April 6, 2002. The main acoustic arrival has been corrected for the duration of the fireball. cC-O res is the computed-observed residuals in sec. d Ri and Rf are the initial and final times of the observed Rayleigh waves. eThe height represents the height along the fireball trajectory that produces the closest time-delay match to the true acoustic arrival based on the ray modeling (see text). The brackets represent the range of possible heights within the modeled range of arrival times. fThe model launch azimuth and altitude are the apparent azimuth and altitude of the best-fit rays launched from the fireball trajectory, with negative altitude representing downward directed rays.
2% later than observed—this strongly suggests that our effective sound velocity was slightly high. However, a path- averaged variation of 1–2% is certainly well within the variability that is expected for effective sound speed (cf. Picone et al. 1997). The best-fit source regions along the fireball path from our modeling all generally fit into the cylindrical-line source blast wave model, whereby acoustic radiation dominantly emerges perpendicular to the main trajectory. In the case of the nearest stations to the fireball path, MOTA and SQTA, the perpendicular condition was met near the actual fireball endpoint where significant ablation and fragmentation occurred. This undoubtedly contributed to the strong acoustic (and Rayleigh) waves detected at those stations, as we expected a strong acoustic coupling at points of major disruption along the fireball path. All the remaining stations had met perpendicularly at much higher heights along the Fig. 27. The deviation of the best-fit ray launch trajectories from the fireball path; most seem to have detected signals originating perpendicular for each seismic station. The best-fit solutions were chosen to have the closest arrival match to the observed airwave from a height of ~40–45 km. Interestingly, the two stations arrivals (see Table 2). The error margins represent the range of showing the greatest deviation from perpendicular acoustic allowed deviations given the spread in modeled arrival timings. paths (FUR and FUORN) also have their best-fit source Entry dynamics and acoustics/infrasonic/seismic analysis of Neuschwanstein 1621 heights at 39–40 km; this may reflect an enhanced acoustic other parts of this work that the majority of the infrasound and energy deposition near this altitude that is perhaps associated seismic signals from Neuschwanstein emanated from below with an extended zone of low-level fragmentation near this ~50 km, we used a mean air temperature of 250.0 K for height, though this is a speculative result in the absence of calculating the constant pressure (density) scale height more constraining data (also see the entry dynamics (=7.317 km) and the constant thermodynamic sound speed discussion above, where the primary modeled fragmentation (=316.96 m/s) with a constant surface pressure (=1.01325 × processes were initiated at ~23 km to explain the observed 105 Pa) as average values over the lowest 50 km in altitude of bolide panchromatic luminosity). the middle latitude atmosphere. In general, these seismic data are compatible with most First and foremost, for a ray theory type of approach to be acoustic energy being radiated as part of a cylindrical line valid, the following uniform duct criterion should be satisfied source blast wave. Secondary events in the seismic record (Ceplecha et al. 1998): may be interpreted to support a fragmentation event near R ≤ 2 ⋅ H2/λ (1) 31 km (though not all stations show this secondary event) and, more weakly, an extended zone of possible where H = the vertical duct thickness; λ = the dominant fragmentation near an altitude of 40 km that was also not seen wavelength of the acoustic wave (at maximum signal in the entry dynamics simulations given earlier. However, amplitude) = τ ⋅
Table 4. Summary of infrasonic evaluations for Neuschwanstein. Type of approach First infrasound arrival: weaka Second infrasound arrival: strongb
Robs = 256 km τ = 0.91 sec; ∆p = 0.775 Pa τ = 0.35 sec; ∆p = 2.68 Pa −2 −2 c Es∞ = 2.08 × 10 kt to 2.76 × 10 kt y = ½ (linear) solution y = ¾ (weak shock) solution −2 d Es∞ = 1.57 × 10 kt d′ = 1099.4 km d′ = 122.3 km e −3 −4 Method a: AFTAC (wave period): Es 3.84 × 10 kt 1.58 × 10 kt e −3 −5 Method b: Line source (wave period): Es 1.45 × 10 kt 3.18 × 10 kt e −3 −5 Method c: Line source (wave amplitude): Es 1.45 × 10 kt 3.18 × 10 kt Method d: Line source (wave period and 48.35 kmf 16.21 kmf amplitude): source height Method e: Iterative blast wave radius solution Multi-valued solution with heights from Multi-valued solution with heights from for matching observations and theory (see text ~14.75–15.25 km and 75–83 km for Ro ≅ ~20.5–22.5 and ~38–44 km for Ro ≅ 10– for details) 10–40 m. (See Fig. 8b.) 40 m. (See Fig. 8a.) aSource altitude search increment = 1.0 km; isothermal, hydrostatic model atmosphere. bSource altitude search increment = 0.50 km; isothermal, hydrostatic model atmosphere. cEntry model source energy estimate (this study; see Table 1entry dynamics solutions). dInitial source energy estimate of Spurn˝ et al. (2002, 2003). eBolide source energy at the source height: not the initial bolide kinetic energy. fThis source height produces a simultaneous matching of the estimated line source energy using either the amplitude or the period approaches, respectively. bolide velocity; M = the Mach number = V/cs; k = the efficiency of ReVelle and Ceplecha (2001a). In contrast, the numerical value accounting for break-up effects (with differential acoustic efficiency was independently calculated collective wake behavior after break-up, k >1); and R = the from first principles using blast wave scaling laws and slant range from the source to the observer, which was done independent, detailed, numerical calculations. Both the with no fragmentation effects included (no modifications differential (and the integral) acoustic efficiency were made in the expression for Ro, i.e., k = 1 ). calculated using the line source blast wave approach given in c. Line source approach: observed amplitude and slant ReVelle (1976), and the former parameter is used directly in range approach including assumed source altitude the analysis that follows. We are quite confident that this effects (Ceplecha et al. 1998). approach is fundamentally correct because the computed power balance is quite reasonable (summing to nearly 100% 3 4 3 over most of the visible bolide trail) and because the Es = 11.5 ⋅⋅πρm ⋅R ⋅()∆pop– ⁄ pzpg ()cs ⁄ V (4) differential acoustic efficiency (which is a significant part of where po−p = the pressure amplitude of the acoustic signal the total power balance, especially at low heights) has been (zero to peak value or of the positive phase of the signal); pz = calculated totally independent of the other differential the ambient pressure at the source generation altitude; and pg efficiencies. Secondly, as will be seen below, the computed = the ambient pressure at the ground. theoretical differential acoustic efficiency allows a very d. Line source approach: observed amplitude and wave reasonable source height estimate to be made for period as well as slant range included with the source Neuschwanstein (at least for the strongest infrasonic arrivals; altitude explicitly calculated to match approach (c) see below). above (ReVelle 1976). In the following, we have assumed negligibly small dissipative effects, i.e., viscous, thermal, internal molecular ∆p /τ = 0.1847 ⋅ p* ⋅ (c /R) (5) o−p s relaxation effects, etc. For relatively large bolides such as where p* = the geometric mean pressure between the source Neuschwanstein, the fundamental blast wave frequency is * altitude and the ground and p = pzpg . sufficiently low that we should expect relatively small e. New line source approach: differential acoustic dissipative effects, as discussed in ReVelle (1976). This fully efficiency limits. justifies our approach at sufficiently low heights (below We have recently performed a total power balance for the ~100 km). In our subsequent treatment, we also assumed that Neuschwanstein bolide based on the entry dynamics the total range to the bolide can be adequately represented by (including the energetics and fragmentation analyses the square root of the square of the horizontal range and of the presented earlier). The full details of this approach will be assumed source height. For close infrasonic detection, this is presented elsewhere since it has just been completed. Briefly, an acceptable approximation, but at progressively larger the computation sums up the total power balance of the ranges, it certainly needs to be examined more carefully, as differential efficiencies of heat, panchromatic light emission discussed in ReVelle (1976). In our analysis, we also have (360–675 nm), acoustical waves (through its kinetic energy neglected the ground reflection factor effect (ReVelle 1976) density), dissociation, and, finally, ionization using a direct that should be between unity (no ground reflection) and twice scaling relationship between the parameters above and the the nominal signal amplitude (if no signal losses due to recently calibrated semi-empirical panchromatic luminous ground penetration occurred due to a finite ground Entry dynamics and acoustics/infrasonic/seismic analysis of Neuschwanstein 1623 impedance). This factor also depends on the elevation arrival of a non-uniform medium (due to air density changes) are angle of the infrasonic signals and cannot simply be evaluated represented above in the function g(z). Slight modifications of in general. However, as a first step, we have examined the the current results are expected for a non-isothermal medium, signal doubling limit and found very little detailed change in and these are currently under investigation. The functional either of the solutions that were determined below (for the relation, g(z) for the air density effects, provides a physical strong and weak infrasonic signals, respectively). explanation for the nonlinear velocity amplitude growth for In addition, the solutions determined below were found wave propagation vertically upward into the atmosphere for a to be multi-valued in general. This is produced by a near-ground source such that the wave kinetic energy density combination of effects due to both source height (through the is conserved (or, equivalently, the concomitant rapid velocity air density) and the total range, which, as discussed above, amplitude decrease for downward wave propagation that also includes a source height component. Although the kinetic results in a rapid evolution toward a linear wave propagation energy density approach described below is new and state). The explanation of the y parameter in Equation 6b is incorporates the differential acoustic efficiency for the first given below. time, in essence, it is fundamentally very similar to methods In the expressions above, the symbols are further defined (c) and (d) above. The major difference is that, in what as: zs = the source height; Hp = the pressure (or density) scale follows below, we have determined the solution numerically height; and do not use the observed wave frequency to constrain the H ≡ −p(z)/(∂p[z]/∂z); ∂p(z)/∂z = −g ⋅ ρ results. Instead, we have only used the wave frequency to p decide whether or not the propagation is in the weakly Ro = the line source blast wave relaxation radius nonlinear or fully linear domain (through the exponent of the (ReVelle 1976); Rg = the range at the ground observation total range to the bolide). point; x = R/Ro = the scaled distance from the source; ∆vo = This method interconnects all of the available amplitude the observed infrasonic perturbation wind (due to the wave): data in one iterative approach and numerically matches the ∆v ≡ ∆p/(ρ ⋅ c )(6e) observed infrasonic acoustic efficiency at Freyung, within a s prescribed tolerance, to the predicted values over a range of which is written in terms of a locally plane, pressure wave possible source heights. A tolerance of 0.1% was assumed amplitude, ∆p, the ambient air density, ρ, and the local sound over altitude search intervals from 1.0 km (for the weak speed, cs. infrasonic signals) to 0.50 km (for the strong infrasonic ∆v (z, x = 10) = (2.0 ⋅ KE [z]/ρ[z])1/2 (6f) signals), respectively. Our entry dynamics results for the p dp initial pre-atmospheric source parameters for Neuschwanstein ∆vp(z, x = 10) = the predicted infrasonic perturbation wind; (mass, velocity, kinetic energy, differential acoustic KEdp(z) = the wave kinetic energy density at the source (first efficiency) have been least-squares curve-fitted and properly defined at x = 10). formulated in a new computer code to reliably perform this The perturbation wind due to the wave and its pressure new numerical approach. The entry model predictions are amplitude (see below) is also directly related to the already known to agree quite well with other independent differential acoustic efficiency, εtheory(z, x = 10), because of estimates of the parameters of Neuschwanstein such as our definition: ground-based camera and radiometer data, but in general, this ε (z, x = 10) ≡ KE (z)/(KE [z]/V [z]) (6g) new approach will interconnect all of these data, including theory dp bolide ol satellite data, for the first time, in a self-consistent manner. εtheory(z, x = 10) = the wave kinetic energy density/(bolide Our new numerical results are presented in Figs. 8a and 8b and kinetic energy/source deposition volume); KEbolide[z] = the are summarized in Table 4. bolide kinetic energy as a function of height; Vol[z] = the The fundamental analytical expressions summarizing source deposition volume as a function of height: this type of approach can be written as: 2 Vol = π ⋅ Ro (z) ⋅ l(z) (6h) ∆v = ∆v (z, x = 10) ⋅ f(R) ⋅ g(z) (6a) o p defined as energy deposited at x = 1; l(z) = line source length. f(R) = ([10.0 ⋅ R ]/R )y = (10.0/x)y (6b) o g l(z) = ∆z/sinθ (6i) g(z) = (ρ [z = 0]/ρ[z ])1/2 (6c) o s where θ = the horizontal entry angle of the bolide. and, for an isothermal, hydrostatic atmosphere, Equation 6c The theoretical differential acoustic efficiency for can be written in the form: Neuschwanstein is also available from our entry dynamics results in Fig. 6 in the least-squares, curve-fitted form: 1/2 (ρobs[z = 0]/ρ[zs]) = exp(zs/[2Hp]) (6d) ∴ εtheory(z, x = 10) = 0.9137 ⋅ exp(−0.1609 ⋅ z) (6j) 2 where Hp = constant, and the correction terms for the effects where z is in km and r = 0.9046495. 1624 D. O. ReVelle et al.
We have also directly computed the theoretical wave be a linear wave at the observation point, while the second kinetic energy density at the source using Equation 6j: infrasonic arrival was predicted, technically, to have remained a small amplitude weak shock wave during its downward KE (z) ≡ 1/2 ⋅ ρ ⋅ (∆v )2 = ε (z, x = 10) dp p theory propagation. Note that this prediction in Equation 6m relies ⋅ (KE [z]/V [z]) (6k) bolide ol not only on a small wave amplitude relative to the ambient Thus, we have changed variables from Equation 6g from value but also on a sufficiently long wave period to achieve the wave kinetic energy density directly to the perturbation wave propagation in a “linearized” state. wind due to the wave (which was, instead, directly evaluated Equation 6a resulted directed from the fact that the using either the ground-observed or source height predicted differential acoustic efficiency at the source, when properly pressure wave amplitude for locally plane waves). This corrected for range and air density variations, should be the change allowed us to perform iterative calculations to obtain same as the observed infrasonic differential acoustic solutions for the possible blast wave radius values as a efficiency. Since both of these differential efficiency function of height considered as a free parameter that would quantities contain the same divisor, namely, the bolide kinetic allow a self-consistent matching of the predicted and energy at any height per unit deposition volume (x = 1), this observed wave properties (indicated in Figs. 8a and 8b for the divisor initially cancels on both sides of Equation 6a. strong and weak infrasonic signals, respectively). The However, to evaluate the theoretical wave kinetic energy explicit entry dynamics solution for the blast radius as a density as a function of possible source heights (and, function of height (including fragmentation effects) is eventually, the perturbation wind due to the wave), the bolide indicated in Fig. 7. kinetic energy per unit deposition volume as a function of The observed differential acoustic efficiency, εobs, is also height was needed in combination with the readily available available from the infrasonic data and can be defined as: differential acoustic efficiency. This was accomplished by first multiplying the curve fitted ε (z, x = 10) expression ε = 1/2 ⋅ ρ ⋅ (∆v)2/(KE [z]/V [z]) = 1/2 ⋅ ∆p2 theory obs bolide ol for Neuschwanstein by the predicted expression for the 2 /(ρ ⋅ cobs )/(KEbolide[z]/Vol[z]) (6l) bolide’s kinetic energy(z)/source deposition volume(z). This with the latter form also written for a locally plane wave so later expression was determined by individually curve fitting that it could be transformed into the observed pressure wave both the predicted mass, m, and the velocity, V, as a function amplitude. of height separately and forming the product ½ m ⋅ V2. Thus, To calculate the final results, only the numerator of εobs KEbolide(z)/Vol(z) was ultimately needed for all possible was necessary since the bolide kinetic energy/deposition source heights to complete the final computations using all of volume cancels when the predicted and observed differential the variables. The denominator of this latter expression was acoustic efficiencies are compared in Equation 6a. also determined using a curve fit of the predicted blast wave The range dependent function in Equation 6b, y, has radius as a function of height (along with a computation of limits of y = −3/4 as x → ∞, respectively, which is the the line source length as well). The final results are slightly appropriate value for the decay of the pressure (or velocity) sensitive to the assumed threshold acceptance criterion and to amplitude of weakly nonlinear acoustic waves in a uniform the size of the altitude search interval, but the presented medium (ReVelle 1976), or y = −1/2 as x → ∞ for “linear,” results are quite reliable over a range of threshold acceptance small amplitude waves. To evaluate this possibility in greater values. detail, we next computed the 10% wave propagation Evaluating the expressions above in an iterative manner distortion distance for nonlinear wave “steepening” effects to using the observed horizontal range and for various slant be important (ReVelle 1976), namely: ranges calculated as a function of the source height for an hydrostatic, isothermal atmosphere, we have produced plots of d’ = c ⋅ τ/(34.3 ⋅ ∆p/p )(6m) s o the possible self-consistent values of the nonlinear blast wave If the propagation distance to the observation point is relaxation radii solutions that are indicated in Figs. 8a and 8b. >d’, then the wave behavior is deemed linear; otherwise, the Only over a narrow height range of ~20–22 and 38–45 km are weak shock approximation is maintained. For these the infrasonic observations in agreement with the entry respective limits in a uniform medium, the parameter, y, can dynamics and other results for the second infrasonic (strong) be summarized as: signal arrival. This is also a similar height range to those deduced earlier, based solely on ray tracing techniques, and to y = ½ if the propagation is “linear;” the results found using method (d) above (~16.2 km). For the y = ¾ if the propagation is weakly nonlinear (6n) weaker infrasonic signals, there is much more uncertainty, but Due to the change in both the observed period at a source height of ~15 km and also 75–83 km has been maximum amplitude and the observed maximum pressure determined using this approach. The lower of these two source amplitude of each of the two infrasonic arrivals for heights is probably not very reliable because our curve fit for Neuschwanstein, the first infrasonic arrival was predicted to the predicted kinetic energy of Neuschwanstein is Entry dynamics and acoustics/infrasonic/seismic analysis of Neuschwanstein 1625 progressively less accurate below ~18 km. These results do not self-consistently arrived from ~15 and from 75–83 km, while agree with either the ray tracing results, results observed from the strong infrasound signals were shown to have arrived the bolide luminous path, or with the approach using Equation from possible source heights of 16–22 km and 38–44 km, 5 listed in Table 4, which will be further examined below. respectively (multi-valued solution). The former weak The source energy plotted in Figs. 8a and 8b was infrasound height estimates using method (e) are not very calculated using the expression for the kinetic energy of a reliable, however, and require further analysis. In addition, spherical non-fragmenting bolide written explicitly in terms from time delay ray tracing analyses using the seismic data of the relaxation blast radius for an ideal line source, namely: alone (see Table 3), we have also independently determined a source height extreme range for the main arrival of 18–52 km, 2 3/2 3 3/2 Es = 1/2m ⋅ V = ([π /2] ⋅ [1/(8k )] ⋅ [1/Sf ]) which varies substantially between seismic stations. In 3 3 ⋅ (ρm ⋅ Ro ⋅ [cs /V]) (6o) addition, there is a secondary maximum seismic time-delay arrival solution with a consistent source height near 30 km. where Sf = shape factor, which reduces for a sphere (Sf = This latter source height has only been determined at a few of 1.209), and where k = 1, i.e., no fragmentation effects (see the seismic stations but is also in quite reasonable agreement Equation 3b above) to the standard expression: with the moving point-source, ray tracing results determined for the weaker infrasound signals, as described earlier. The E = (π/12) ⋅ ρ ⋅ Ro3 ⋅ (c 3/V) (6p) s m s majority of all of the height estimates are in general Note that, for k >1 (collective wake behavior), the agreement that the ground-based recordings of the original predicted values of Es in Figs. 8a and 8b are rapidly reduced blast wave signals emanated from regions of the trajectory further due to the strong dependence on the precise value of k. where the brightest luminosity was also measured and where The value of k is a function of height, however, only over part significant fragmentation effects occurred (which is known of the trajectory, i.e., for most purposes, k is essentially unity from the flaring of the light curve), which is a very reassuring over a large portion of the entry. feature of our analyses. This result is extremely encouraging since it combines for the first time the entry dynamics, the ground-based CONCLUSIONS photographic and radiometer data, and the infrasound/seismic data together in one coherent and self-consistent summary for We have produced entry model simulations of the a bolide. Even satellite data can readily be included in this Neushwanstein meteorite fall of April 6, 2002 using the type of analysis. nominal set of entry parameters provided by Spurn˝ et al. (2002, 2003). Very good agreement in source heights, probable DISCUSSION dynamics, energetics, and fragmentation behavior has been found using a number of different kinds of data and using a Given the implications of Neuschwanstein and its number of fundamentally different techniques. Source energy connection to the Pribram meteorite fall of April 7, 1959, the estimates do not exceed 0.0276 kt, and an average value of importance of its proper modeling and interpretations cannot ~0.02 kt is in good agreement with that of Spurn˝ et al. (2002, be overstated. We have determined that the photographic and 2003), namely, 0.0157 kt (1 kt = 4.185 × 1012 J). Moving point radiometer evidence, as well as the infrasound and seismic source and line source ray tracing techniques have been applied evidence, are all in general agreement about the initial size of to this case, and generally good agreement between these this fireball (<0.30–0.33 m or ~400–530 kg for a sphere of techniques has been found. Finally, the entry dynamics have <5% uniform volume-weighted porosity or an initial kinetic been directly connected, using a numerical technique, to the energy <0.016–0.028 kt.). We have also deduced reliable infrasonic and seismic data recorded in association with the source heights for the infrasound/seismic signals using both entry of Neuschwanstein. Excellent agreement has been found moving point source and line source ray tracing techniques as when comparing the ray tracing source height results with the well as wave propagation methods in an independent manner. theoretical differential acoustic efficiency numerical results for At least, for the strongest infrasonic signals, these approaches the strongest infrasonic signals. are in good agreement with one another regarding the altitude range from which these signals emanated. Our source height Acknowledgments–D. O. ReVelle would like to thank US results can be summarized as follows. DOE HQ (NN-22) and the local LANL ISR-RD office From a moving point-source model using the ray tracing (specifically Mr. Mark Hodgson) for their support of this propagation time delay approach, we have ascertained that the work over the past year. P. G. Brown wishes to thank the weak and strong infrasound signals arrived from ~16–22 km Canada Research Chair Program and the Natural Sciences and 30–32 km, respectively. From our new kinetic energy and Engineering Research Council of Canada for funding. density, wave-amplitude method described in method (e) above, the weak infrasound signals have been found to have Editorial Handling—Dr. Donald Brownlee 1626 D. O. ReVelle et al.
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